This invention relates to determining minority carrier diffusion lengths, and particularly to fast and accurate determination of minority carrier diffusion lengths.
The performance and reliability of semiconductor electronic and optoelectronic devices, and the integrated circuits into which they are incorporated, depends upon the purity of the semiconductor from which the devices are made. In particular, the level of heavy metal contaminants (e.g., Fe, Cr, and other metals) which may be introduced into the semiconductor during manufacturing and processing degrades performance and reduces the manufacturing yield.
One measure of semiconductor contamination is the minority carrier diffusion length, L. This parameter is the effective distance that excess minority carriers diffuse into a semiconductor during their lifetime. The value of minority carrier diffusion length is used as an indicator of the purity of semiconductor materials. L gives a measure of the contaminant concentration in the semiconductor because heavy metals function as recombination centers which reduce the minority carrier lifetime. As a result, higher concentrations of contaminants decrease the minority carrier diffusion length. Typically, the diffusion length in silicon wafers is measured at various stages of fabrication of microelectronic chips to measure the concentration of potentially harmful impurities inadvertently introduced into the wafer. Frequent monitoring of the minority carrier diffusion length helps to identify when a given process or a given tool starts to contaminate wafers above a permissible level. Preventive maintenance of processing equipment or replacement of chemicals done at this stage helps to avoid large manufacturing loses.
A general technique for measuring diffusion length includes directing a light signal onto a semiconductor to create a surface photovoltage. A surface photovoltage results when the energy of the incident photons is above the semiconductor band gap such that it produces excess carriers (holes and electrons). As a result of photogeneration, recombination, and diffusion, a concentration profile of the excess carriers is established beneath the surface of the semiconductor wafer. Larger excess carrier concentrations near the surface of the semiconductor reduce the electric field of the surface-space charge region and thereby produce larger surface photovoltage signals.
In certain diffusion length measurements, intensity modulation of the light signal produces an ac-surface photovoltage which, in turn, produces an ac-electrical signal in a capacitor formed by the semiconductor wafer and an electrode placed near the semiconductor""s surface. The ac-electrical signal is subsequently measured using a lock-in amplifier tuned to the light modulation frequency to determine the surface photovoltage. Devices for determining diffusion length via surface photovoltage measurements are described in U.S. patent application Ser. Nos. 5,025,145 and 5,663,657, the contents of which are herein incorporated in their entirety.
Typically, the diffusion length measuring techniques implemented in commercial instruments use a sequence of successive illuminations of the semiconductor with monochromic beams each being intensity modulated at the same frequency but having different wavelengths. Different wavelengths of light generate minority carriers in regions extending to different depths beneath the wafer surface. The corresponding ac-surface photovoltages produced by the different wavelengths are measured sequentially, i.e., one after another, and the resulting data of the surface photovoltage, V, vs. the excitation depth, z (i.e. the light penetration depth), are then used to calculate the minority carrier diffusion length.
The American Society for Testing and Materials (ASTM) recommends two methods to determine diffusion length by employing successively measured surface photovoltage signals. See, for example, ASTM F391-96. In both of these methods, the diffusion length calculation is based on the steady-state equation for excess minority carrier concentration at the surface and is valid for low light modulation frequencies and for minority carrier diffusion lengths that are short in comparison to the semiconductor wafer thickness.
This steady-state equation is given by the expression:                               Δ          ⁢                      xe2x80x83                    ⁢          n                =                  Φ          ⁢                                    1              -              R                                      (                                                D                  /                  L                                -                S                            )                                ⁢                      1                          (                              1                +                                  zL                                      -                    1                                                              )                                                          (        1        )            
where xcex94n is the excess minority carrier concentration; L is the diffusion length; z is the penetration depth; "PHgr" is the incident photon flux; R is the reflectivity of the semiconductor; D is the minority carrier diffusion constant, D=kT/qxcexc, where k is Boltzman""s constant, T is the temperature, q is the elemental charge, and xcexc is the minority carrier mobility; and S is the surface recombination velocity on the front surface of the semiconductor. This expression is derived in Moss, J. Electronics and Control, 1, 126, (1955).
In the constant magnitude method, one of the ASTM-recommended methods, the photon flux, "PHgr", is measured and it is adjusted to obtain the same surface photovoltage value for each wavelength. The method assumes that the excess carrier concentration, xcex94n is constant because the photovoltage is constant. The diffusion length is then obtained, using Equation (1), for xcex94n=const. From a plot of the photon flux, "PHgr", as a function of the light penetration depth, z, the diffusion length is determined as the intercept value, L=xe2x88x92zint at "PHgr"=0. The constant magnitude method is further discussed, for example, in Goodman, J. Appl. Phys. Vol. 32, p. 2550, 1961, and U.S. Pat. No. 4,333,051.
The second ASTM-recommended method, the linear constant photon flux, relies on measurements of the surface photovoltage only. These measurements are performed with low light intensity so that resulting surface photovoltage is a linear function of the photon flux. Under these conditions, the surface photovoltage is directly proportional to the minority carrier concentration, or V=constxe2x80xa2xcex94n, where the constant depends on the semiconductor doping and the surface charge, but does not depend on the photon flux. In this method the measuring apparatus is built in such a way that the effective photon flux entering a semiconductor, "PHgr"eff="PHgr"(1xe2x88x92R), is constant for all wavelengths and, thus, for all penetration depths, z. For short L values, the diffusion length is obtained by plotting the inverse of the photovoltage signal, "PHgr"eff/V, as a function of penetration depth, z. An intercept value, at "PHgr"eff/V=0 gives L=zint. This method is further discussed in U.S. Pat. Nos. 5,025,145 and 5,177,351, and in Solid State Technol. 35, 27 (1992) and in Semicond. Sci. Technol. 7, A185 (1992). An improved version of this method suitable for long diffusion length, i.e., when the minority carrier diffusion length exceeds the wafer thickness, is also discussed in U.S. Pat. No. 5,663,657 and ASTM stock # STP1340 p. 125 (1998), by Lagowski et. al.
The present invention provides a surface photovoltage (SPV) apparatus and method for measuring the minority carrier diffusion length, L, which is faster, e.g., at least twice as fast, than existing methods. The enhancement in speed is achieved by replacing a plurality of successive surface photovoltage measurements with a single simultaneous measurement of all surface photovoltage signals (for all penetration depths) at the same moment of time.
The apparatus of the invention uses a linear constant photon flux method described in previous section to determine the minority carrier diffusion length. The apparatus illuminates simultaneously a semiconductor wafer with a beam containing an entire set of wavelengths rather than with consecutive beams of different wavelengths. Each component of the beam, i.e., each monochromatic wavelength in the set, is modulated with a different frequency, (i.e. xcex1 with the frequency f1, xcex2 with the frequency f2, etc), rather than with the same frequency. Amplitudes and phases of all SPV signals generated by each different wavelength are simultaneously measured using parallel lock-in amplifier inputs tuned respectively to different frequencies. For example, the photovoltage amplitude Vf1, and the phase xcfx86f1 are measured at frequency f1 and the photovoltage Vf2 and the phase xcfx86f2 are measured at frequency f2. In general, each of the monochromatic wavelengths has a different center wavelength and a linewidth, full-width at half-maximum (FWHM), such as equal to or less than about 15 nm, 10 nm, or 5 nm.
In one aspect, the invention features a method of analyzing semiconductor samples by determining minority carrier diffusion length. The method includes illuminating simultaneously a region of the semiconductor with light including a plurality of wavelengths, wherein each wavelength within the plurality is modulated at a different frequency, and a flux of the light being substantially constant for all wavelengths and at a level to generate a surface photovoltage as linear function of the flux; detecting simultaneously a surface photovoltage produced in the semiconductor for each wavelength of the plurality of wavelengths in the light; correcting the frequency dependence of the surface photovoltages to produce frequency corrected surface photovoltages; and calculating the minority carrier diffusion length with the frequency corrected surface photovoltages.
In another aspect, the invention features, a method of analyzing semiconductor samples by determining minority carrier diffusion length. The method includes illuminating simultaneously a region of the semiconductor with light including a plurality of wavelengths, wherein each wavelength within the plurality of wavelengths is modulated at a different frequency; and detecting simultaneously a surface photovoltage produced in the semiconductor by at least two of the plurality of wavelengths in the light. The method can further include adjusting a flux of each wavelength in the light until the flux is substantially constant for all wavelengths and at a level where surface photovoltage produced by illumination is a linear function of the flux. The method can also include correcting the frequency dependence of the detected surface photovoltages to produce frequency corrected surface photovoltages, and calculating the minority carrier diffusion length with the frequency corrected surface photovoltages.
Embodiments of these aspects may include one or more of the following. The surface photovoltages are simultaneously detected by an electrode placed in proximity to the illuminated site on the semiconductor. Each of the surface photovoltages monitored by in monitoring the amplitudes of surface photovoltages detected via the electrode at each of the different modulation frequencies of the light. The method further includes monitoring the phases of the surface photovoltages at each of the different modulation frequencies of the light. Correcting the frequency dependence includes using at least one monitored phase to adjust the amplitude of at least one surface photovoltage. The phase and the amplitude to be adjusted are monitored at the same modulation frequency. Calculating the minority carrier diffusion length includes analyzing the frequency corrected surface photovoltages as a function of light penetration depth. The light penetration depth is given by
z=[84.732/xcex+(0.110/xcexxe2x88x920.068)(Twxe2x88x92293)xe2x88x9276.417]xe2x88x922
where Tw is the wafer temperature and xcex is the wavelength of light. Determining L, the minority carrier diffusion length, further includes fitting the surface photovoltage for each light penetration depth to V=const.xc2x7xcfx86effxc2x7f(z) where             f      ⁡              (        z        )              =                  1                  1          -                                    z              2                        /                          L              2                                          ⁡              [                  1          -                                    (                              B                /                L                            )                        ⁢            z                          ]              ,      B    =                            (                      v            /                          S              b                                )                ⁢        shin        ⁢                  xe2x80x83                ⁢                  h          (                                    T              /              L                        +                          cos              ⁢                              xe2x80x83                            ⁢                              h                ⁡                                  (                                      T                    /                    L                                    )                                                                                          sin          ⁢                      xe2x80x83                    ⁢                      h            ⁡                          (                              T                /                L                            )                                      +                              (                          v              /                              S                b                                      )                    ⁢          cos          ⁢                      xe2x80x83                    ⁢                      h            ⁡                          (                              T                /                L                            )                                            ,
Sb is the back surface recombination velocity, and vxe2x89xa1D/L is the minority carrier diffusion velocity. The minority carrier diffusion length is determined via the expression L=(z1xe2x88x92r21z2)/(r21xe2x88x921) where r21 is the ratio of the two surface photovoltages associated with the penetration depths z1 and Z2. Correcting the frequency dependence of the surface photovoltages includes recalculating the surface photovoltage to a low frequency limit surface photovoltage. Correcting the frequency dependence of the surface photovoltages includes recalculating the surface photovoltages to a single modulation frequency. The single modulation frequency corresponds to one of the modulation frequencies of the light. Each of the individual wavelengths in the light penetrates into the semiconductor to different penetrating depths beneath the surface of the semiconductor.
In another aspect, the invention features an apparatus for determining the minority carrier diffusion length of a semiconductor sample. The apparatus includes a translatable mount for holding a semiconductor sample; an illuminating system for simultaneously directing a plurality of wavelengths of light each modulated at a different modulation frequency onto a semiconductor sample; and a detector system for simultaneously monitoring a plurality of surface photovoltages at the different modulation frequencies.
In another aspect, the apparatus includes an SPV probe for measuring the surface photovoltage of a semiconductor wafer as described in U.S. Pat. No. 5,663,657. The probe receives the light beam containing a plurality of wavelengths, (at least two,) and passes it to the surface of a semiconductor wafer to induce photovoltage. In a preferred embodiment the probe connects with one end of a fiber optic bundle. On the second end the bundle splits into a series of fiber cables receiving modulated light beams with different wavelengths and also constant light beam from a detrapper.
In another aspect, the apparatus includes an illumination system with multiple wavelength light sources and devices for modulating the intensity of light beams with different frequencies. Preferably the light sources are pre-adjusted such that all wavelengths have the same amplitude of effective photon flux, i.e. xcfx86eff0=xcfx860(1xe2x88x92R). In addition, the illumination system shall permit for changing, xcfx86eff0, in order to obtain the SPV linear condition in which the surface photovoltage is directly proportional to xcfx86eff0. These two aspects are important in order to use the constant photon flux linear SPV method for calculating the minority carrier diffusion length from the measured values of surface photovoltage.
Advantages of the invention include one or more of the following. The new apparatus and method of measuring SPV eliminates errors associated with previous methods caused by changes in surface condition of the wafer between successive measurements. For example, in previous methods, the time delay between successive SPV measurements for different light penetration depths, i.e., different wavelengths of light, creates an error in the minority diffusion length. Thus the method of this invention is more accurate and makes it possible to measure smaller concentrations of metal impurities in substantially shorter times.
The apparatus and method also improves the speed and accuracy of diffusion length mapping of whole semiconductor wafers by producing a distribution pattern of metallic contamination in each wafer to help identify contaminating tools and processes during manufacturing. In previous whole semiconductor wafer mappings, measurements were performed along certain scanning lines (e.g. a ring in case of rotating wafer) first for one wavelength followed by measurements with a second wavelength. The delay, typically 6 seconds, between sequentially measuring the first and second SPV results in changes in the surface condition of the wafer, e.g., static charge created by wafer motion, surface relaxation after previous chemical treatments, and adsorption or desorption caused by ambient changes. These changes alter the SPV signal value and thereby create errors in diffusion length measurement. Errors and corresponding artifact patterns in full wafer mapping produced from previous methods are eliminated in the present invention by performing measurements of surface photovoltage for all wavelengths at exactly the same time.
As used herein, the term surface photovoltage corresponds to a reduction of the surface space charge width during illumination and to its recovery in the dark. The SPV signal amplitude decreases with increasing the light modulation frequency due to a long surface space charge recovery time, xcfx84R. This time can be orders of magnitude larger than the effective minority carrier lifetime and then the time required to establish steady-state concentration profile, xcex94n, in the wafer beneath the surface space charge region. As discussed U.S. Pat. No. 5,977,788, the surface photovoltage can be expressed as
V(xcfx89)=V0(1+xcfx892xcfx84R2)xe2x88x922xe2x80x83xe2x80x83(2)
where xcfx89 is the angular frequency, xcfx89=2xcfx80f and V0 is the surface photovoltage amplitude for fxe2x86x920. The recovery time xcfx84R is related to the SPV signal phase shift by a well known relationship expression derived by NAKHMANSON, in Solid State Electronics, Vol. 18 p. 617(1975):
xcfx89xcfx84R=tanxe2x88x921(xcex94xcfx86)xe2x80x83xe2x80x83(3))
where xcex94xcfx86 is the phase shift between the light modulated with an angular frequency xcfx89 and the SPV signal. The method uses the SPV signal phase shifts, xcex94xcfx86f1, xcex94xcfx86f2, . . . xcex94xcfx86fk that are measured by the lock-in amplifier simultaneously with the amplitude of SPV signal.
The corrected set of SPV signal amplitudes, i.e., V1,V2, . . . , Vk, recalculated to the same frequency (preferably to the lowest light modulation frequency, f1) each corresponding to light penetration depths, i.e., z1, z2, . . . Zk, are used to calculate the minority carrier diffusion length from well-known steady-state SPV equations discussed in U.S. Pat. No. 5,663,657.